Random matrix theory for complexity growth and black hole interiors

Kar, Arjun; Lamprou, Lampros; Rozali, Moshe; Sully, James

doi:10.1007/jhep01(2022)016

Cited by 57 publications

(46 citation statements)

References 71 publications

(152 reference statements)

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“…We will leave a more thorough analysis in two-dimensional CFT for future work. It is also worth emphasizing other proposals for the definition of operator complexity [25,26,27,28,29,30] and it would be interesting to compare them in our context. One can potentially use these to diagnose more fine-grained properties of the collision in the interior.…”

Section: Discussionmentioning

confidence: 99%

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Collisions of localized shocks and quantum circuits

Haehl¹,

Zhao²

2022

Preprint

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We study collisions between localized shockwaves inside a black hole interior. We give a holographic boundary description of this process in terms of the overlap of two growing perturbations in a shared quantum circuit. The perturbations grow both exponentially as well as ballistically. Due to a competition between different physical effects, the circuit analysis shows dependence on the transverse locations and exhibits four regimes of qualitatively different behaviors. On the gravity side we study properties of the post-collision geometry, using exact calculations in simple setups and estimations in more general circumstances. We show that the circuit analysis offers intuitive and surprisingly accurate predictions about gravity computations involving non-linear features of general relativity.

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Section: Discussionmentioning

confidence: 99%

“…of operators [18,19,20,21,22,23,24] and their operator complexity [25,26,27,28,29,30]. Some other related recent studies of the black hole interior using ideas of operator reconstruction include [31,32,33,34,35,36,37] and [38,39,40].…”

Section: Introductionmentioning

confidence: 99%

Collisions of localized shocks and quantum circuits

Haehl¹,

Zhao²

2022

Preprint

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“…If the descent of the Lanczos sequence had a slightly convex profile, the region where the strength of the fluctuations becomes comparable to the mean value on top of which they are added would be pushed towards the right. In fact, the analytical expression for the Lanczos sequence in RMT at large size has this feature [19]: the quasi-linear descent gets eventually modified by a square-root behavior. With this motivation, we use the following Ansatz for the toy Lanczos sequence:…”

Section: Disordered Sequence With Ascent and Quasi-linear Convex Descentmentioning

confidence: 99%

“…It also does not depend on a tolerance parameter as gate complexity does [1], or on a penalty metric as geometric complexity does [11]. Other recent work related to the study of K-complexity includes [17][18][19][20][21][22][23]. In particular, works like [17,19,22,24] have applied it to the realm of holographic conformal field theory.…”

Section: Introductionmentioning

confidence: 99%

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Krylov Localization and suppression of complexity

Rabinovici,

Sánchez-Garrido,

Shir

et al. 2021

Preprint

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A notion of quantum complexity can be effectively captured by quantifying the spread of an operator in Krylov space as a consequence of time evolution. Complexity is expected to behave differently in chaotic many-body systems, as compared to integrable ones. In this paper we investigate Krylov complexity for the case of interacting integrable models at finite size and find that complexity saturation is suppressed as compared to chaotic systems. We associate this behavior with a novel localization phenomenon on the Krylov chain by mapping the theory of complexity growth and spread to an Anderson localization hopping model with off-diagonal disorder, and find that increasing the amount of disorder effectively suppresses Krylov complexity. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain, and show that the same behavior results from a phenomenological model that we define. This model captures the essential features of our analysis and is able to reproduce the behaviors we observe for chaotic and integrable systems via an adjustable disorder parameter.

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Spread complexity and topological transitions in the Kitaev chain

Caputa

Gupta

Haque

et al. 2023

J. High Energ. Phys.

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A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.

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Random matrix theory for complexity growth and black hole interiors

Cited by 57 publications

References 71 publications

Collisions of localized shocks and quantum circuits

Collisions of localized shocks and quantum circuits

Krylov Localization and suppression of complexity

Spread complexity and topological transitions in the Kitaev chain

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